Strategic market games with cyclic endowments

We consider an infinite horizon cash-in-advance market economy with symmetric agents. In each stage, a representative agent receives an independent, random endowment from one of k known distributions. The endowment distribution changes cyclically across stages. We suppose that a central bank sets a fixed, nominal interest rate for both borrowing and investing. In equilibrium, the expected rate of inflation across each cycle of length k is strictly greater with random endowments from cyclic distributions than with deterministic endowments.